In a small pan on medium low heat brown the butter on med. low heat. The butter will begin to separate and the milk solids will begin to sizzle. Allow the butter to brown but not burn. It will smell toasted.
Pour into a small ramekin and refrigerate until hardened, about 2 hrs. Can be stored up to a week at this point.
When ready to make frosting remove from refrigerator and allow to sit for 1hr at room temperature.
Whip butter and icing sugar on low in a mixer. Add 2 tbsp. rum and whip the mixture together.